4 papers
Sobolev inequalities for nonlinear Dirichlet forms
Ralph Chill, Burkhard Claus
In this short note we show an equivalence between Sobolev type inequalities and so called isocapacitary inequalities in the context of a large class of nonlinear Dirichlet forms, t…
Domination of nonlinear semigroups generated by regular, local Dirichlet forms
Ralph Chill, Burkhard Claus
In this article we study perturbations of local, nonlinear Dirichlet forms on arbitrary topological measure spaces. We show that the semigroup of a local Dirichlet form \(\mathcal{…
Energy Spaces, Dirichlet Forms and Capacities in a Nonlinear Setting
Burkhard Claus
In this article we study lower semicontinuous, convex functionals on real Hilbert spaces. In the first part of the article we construct a Banach space that serves as the energy spa…
Realization of the fractional Laplacian with nonlocal exterior conditions via forms method
Burkhard Claus, Mahamadi Warma
Let $Ω\subset\RR^n$ () be a bounded open set with a Lipschitz continuous boundary. In the first part of the paper, using the method of bilinear forms, we give a rigorous ch…